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ctbmv.f(3)				      LAPACK				       ctbmv.f(3)

NAME
       ctbmv.f -

SYNOPSIS
   Functions/Subroutines
       subroutine ctbmv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
	   CTBMV

Function/Subroutine Documentation
   subroutine ctbmv (characterUPLO, characterTRANS, characterDIAG, integerN, integerK, complex,
       dimension(lda,*)A, integerLDA, complex, dimension(*)X, integerINCX)
       CTBMV Purpose:

	    CTBMV  performs one of the matrix-vector operations

	       x := A*x,   or	x := A**T*x,   or   x := A**H*x,

	    where x is an n element vector and	A is an n by n unit, or non-unit,
	    upper or lower triangular band matrix, with ( k + 1 ) diagonals.

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		      On entry, UPLO specifies whether the matrix is an upper or
		      lower triangular matrix as follows:

			 UPLO = 'U' or 'u'   A is an upper triangular matrix.

			 UPLO = 'L' or 'l'   A is a lower triangular matrix.

	   TRANS

		     TRANS is CHARACTER*1
		      On entry, TRANS specifies the operation to be performed as
		      follows:

			 TRANS = 'N' or 'n'   x := A*x.

			 TRANS = 'T' or 't'   x := A**T*x.

			 TRANS = 'C' or 'c'   x := A**H*x.

	   DIAG

		     DIAG is CHARACTER*1
		      On entry, DIAG specifies whether or not A is unit
		      triangular as follows:

			 DIAG = 'U' or 'u'   A is assumed to be unit triangular.

			 DIAG = 'N' or 'n'   A is not assumed to be unit
					     triangular.

	   N

		     N is INTEGER
		      On entry, N specifies the order of the matrix A.
		      N must be at least zero.

	   K

		     K is INTEGER
		      On entry with UPLO = 'U' or 'u', K specifies the number of
		      super-diagonals of the matrix A.
		      On entry with UPLO = 'L' or 'l', K specifies the number of
		      sub-diagonals of the matrix A.
		      K must satisfy  0 .le. K.

	   A

		     A is COMPLEX array of DIMENSION ( LDA, n ).
		      Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
		      by n part of the array A must contain the upper triangular
		      band part of the matrix of coefficients, supplied column by
		      column, with the leading diagonal of the matrix in row
		      ( k + 1 ) of the array, the first super-diagonal starting at
		      position 2 in row k, and so on. The top left k by k triangle
		      of the array A is not referenced.
		      The following program segment will transfer an upper
		      triangular band matrix from conventional full matrix storage
		      to band storage:

			    DO 20, J = 1, N
			       M = K + 1 - J
			       DO 10, I = MAX( 1, J - K ), J
				  A( M + I, J ) = matrix( I, J )
			 10    CONTINUE
			 20 CONTINUE

		      Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
		      by n part of the array A must contain the lower triangular
		      band part of the matrix of coefficients, supplied column by
		      column, with the leading diagonal of the matrix in row 1 of
		      the array, the first sub-diagonal starting at position 1 in
		      row 2, and so on. The bottom right k by k triangle of the
		      array A is not referenced.
		      The following program segment will transfer a lower
		      triangular band matrix from conventional full matrix storage
		      to band storage:

			    DO 20, J = 1, N
			       M = 1 - J
			       DO 10, I = J, MIN( N, J + K )
				  A( M + I, J ) = matrix( I, J )
			 10    CONTINUE
			 20 CONTINUE

		      Note that when DIAG = 'U' or 'u' the elements of the array A
		      corresponding to the diagonal elements of the matrix are not
		      referenced, but are assumed to be unity.

	   LDA

		     LDA is INTEGER
		      On entry, LDA specifies the first dimension of A as declared
		      in the calling (sub) program. LDA must be at least
		      ( k + 1 ).

	   X

		     X is COMPLEX array of dimension at least
		      ( 1 + ( n - 1 )*abs( INCX ) ).
		      Before entry, the incremented array X must contain the n
		      element vector x. On exit, X is overwritten with the
		      tranformed vector x.

	   INCX

		     INCX is INTEGER
		      On entry, INCX specifies the increment for the elements of
		      X. INCX must not be zero.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Further Details:

	     Level 2 Blas routine.
	     The vector and matrix arguments are not referenced when N = 0, or M = 0

	     -- Written on 22-October-1986.
		Jack Dongarra, Argonne National Lab.
		Jeremy Du Croz, Nag Central Office.
		Sven Hammarling, Nag Central Office.
		Richard Hanson, Sandia National Labs.

       Definition at line 187 of file ctbmv.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			       ctbmv.f(3)
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